Least Common Multiple (LCM) of 126 and 171
The least common multiple (LCM) of 126 and 171 is 2394.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 126 and 171?
First, calculate the GCD of 126 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 171 = 0 remainder 126 |
| 2 | 171 ÷ 126 = 1 remainder 45 |
| 3 | 126 ÷ 45 = 2 remainder 36 |
| 4 | 45 ÷ 36 = 1 remainder 9 |
| 5 | 36 ÷ 9 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 143 | 2860 |
| 47 and 164 | 7708 |
| 121 and 83 | 10043 |
| 107 and 64 | 6848 |
| 148 and 87 | 12876 |